{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-8, 3, -4, -4, -8],\n [-15, 2, 5, -7, 4],\n [-6, -2, 2, -2, -8],\n [-7, -13, 3, 4, 0],\n [-10, -10, -14, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-14, -2, -12, 6, 8],\n [-2, -3, -8, 4, -4],\n [-12, -8, 13, 1, 2],\n [6, 4, 1, 15, 2],\n [8, -4, 2, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-12, 4, 0, 2, -9],\n [4, 12, -6, -11, -12],\n [0, -6, 12, 0, 3],\n [2, -11, 0, -8, -2],\n [-9, -12, 3, -2, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -8, 5, 2, -6],\n [-8, -4, 0, -8, 0],\n [5, 0, 7, 6, 8],\n [2, -8, 6, 5, -4],\n [-6, 0, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/150 * A where A =\n[[1, -2, 8, -10, -2],\n [-2, -1, -6, 10, 14],\n [8, -6, 15, 10, 0],\n [-10, 10, 10, -14, -8],\n [-2, 14, 0, -8, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, -2, 6, 2, 6],\n [-2, 15, 2, -4, 4],\n [6, 2, 1, 1, 2],\n [2, -4, 1, 9, 11],\n [6, 4, 2, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 6, 8, 0, 1],\n [6, 3, -10, 4, 3],\n [8, -10, -11, -4, 0],\n [0, 4, -4, -1, -11],\n [1, 3, 0, -11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 5, -1, 3, -10],\n [8, -10, -2, 15, -15],\n [7, -4, 0, 7, -3],\n [11, 11, 3, 6, 2],\n [7, 2, -3, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2971", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[8, -7, -14, 4, 8],\n [-7, 2, 3, -9, -14],\n [10, -15, 8, -15, 15],\n [-3, 13, -11, 6, 9],\n [9, 15, 4, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 0, 2, 7, 8],\n [0, -4, 4, 0, -6],\n [2, 4, -7, -4, -2],\n [7, 0, -4, 9, 10],\n [8, -6, -2, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 4, -5, 11, 6],\n [4, -15, -4, -3, -8],\n [-5, -4, -1, -11, 5],\n [11, -3, -11, -8, 0],\n [6, -8, 5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -6, 0, 6, -6],\n [-6, -2, 10, -8, -6],\n [0, 10, 11, -4, -6],\n [6, -8, -4, 6, 0],\n [-6, -6, -6, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 7, -15, 8, 13],\n [-3, -15, -14, -13, -6],\n [-5, -6, -5, -1, 7],\n [6, 9, -1, -7, 10],\n [3, 6, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, -6, 0, 2, -6],\n [-6, 0, -6, 1, 2],\n [0, -6, -15, 2, 8],\n [2, 1, 2, -15, -6],\n [-6, 2, 8, -6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 3, 3, -11, -15],\n [0, -9, 2, 11, 2],\n [0, 0, -12, 14, 13],\n [0, 0, 0, 5, 15],\n [0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-185", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-11, -3, 0, 7, 2],\n [-10, -8, 7, 8, 8],\n [13, -15, 15, 0, 1],\n [4, 14, -10, -3, 14],\n [-4, -7, -3, 4, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, -3, 3, 1, 2],\n [-3, -11, 8, -11, -8],\n [3, 8, 11, 6, 8],\n [1, -11, 6, -7, -1],\n [2, -8, 8, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-314", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -15, -2, 0, 2],\n [-12, 8, -14, -14, -13],\n [-7, 10, 13, 10, -11],\n [0, 8, -4, 0, -14],\n [-10, -4, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the inverse of matrix 1/150 * A where A =\n[[6, 8, 5, 8, -6],\n [8, -14, -3, -11, 10],\n [5, -3, 7, 6, -3],\n [8, -11, 6, 7, -2],\n [-6, 10, -3, -2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-6, 0, 5, 5, -14],\n [2, -11, -2, -5, 13],\n [-5, 9, 2, -11, -2],\n [7, 10, 2, 13, -13],\n [-6, 7, 1, -11, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -7, -1, 4, -15],\n [0, 15, -9, -1, 5],\n [0, 0, 1, -12, -7],\n [0, 0, 0, 11, -12],\n [0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3313", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, -8, 0, 1, 2],\n [-8, 13, -12, -2, -10],\n [0, -12, -3, 0, -10],\n [1, -2, 0, -5, 5],\n [2, -10, -10, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[3, 8, 8, -2, -10],\n [8, -14, 0, 2, 14],\n [8, 0, 10, -6, 5],\n [-2, 2, -6, 13, -3],\n [-10, 14, 5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 8, 10, -3, -7],\n [0, -7, -12, -1, 3],\n [0, 0, 10, -1, -4],\n [0, 0, 0, -14, -13],\n [0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (5, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -14, -9, -10, -6],\n [-3, -14, -13, 6, 4],\n [-4, -12, 14, -5, -12],\n [-10, 8, 8, -15, 8],\n [-3, 2, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-209", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, -4, -9, 6, 10],\n [-4, -6, 0, -3, 0],\n [-9, 0, -12, 0, 14],\n [6, -3, 0, 9, 10],\n [10, 0, 14, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-12, 6, -15, 1, -12],\n [3, 0, -2, -8, -15],\n [12, -15, 15, 15, 0],\n [8, 11, -8, -11, 3],\n [-2, 8, 13, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/150 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, 0, 6, 10, -4],\n [0, -13, 4, -2, 4],\n [6, 4, 7, -2, -6],\n [10, -2, -2, -13, -5],\n [-4, 4, -6, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -8, 15, 1, -10],\n [0, -6, 4, 15, 5],\n [0, 0, -13, 2, -15],\n [0, 0, 0, -6, -15],\n [0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -1, -13, 11, 13],\n [0, 2, -12, 3, -13],\n [0, 0, -5, -13, 14],\n [0, 0, 0, -7, -3],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1608", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, -4, -12, -1, 0],\n [14, -15, 9, -15, 10],\n [1, 10, 5, -1, 2],\n [11, 9, -11, 11, 5],\n [-5, 8, -11, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[3, 2, -2, 2, -4],\n [0, 13, -12, 5, -14],\n [0, 0, 6, -1, 9],\n [0, 0, 0, 4, 4],\n [0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -9, 3, 8, -15],\n [-9, -8, 0, 4, 11],\n [13, -7, 7, -8, -8],\n [14, -10, 4, -3, -7],\n [3, -6, -10, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -1, -1, -4, 6],\n [-7, 0, 14, 15, 2],\n [-6, -15, 15, 2, -6],\n [-8, 9, -3, 4, -9],\n [2, -5, -14, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, -10, -5, 11, 5],\n [0, -12, -7, 13, 15],\n [0, 0, -8, -2, 7],\n [0, 0, 0, -3, 1],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 0, 5, 4, 2],\n [0, 9, -3, 10, 0],\n [5, -3, 6, -3, 4],\n [4, 10, -3, 15, 0],\n [2, 0, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 5) of the inverse of matrix 1/150 * A where A =\n[[-4, -4, 0, 1, 1],\n [-4, -3, -2, -3, 0],\n [0, -2, 2, 14, -2],\n [1, -3, 14, 1, -5],\n [1, 0, -2, -5, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/150 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, 13, 0, 7, 10],\n [-7, 13, -15, 10, 10],\n [6, 3, 9, -4, -8],\n [-7, 8, 2, 2, -14],\n [-4, 13, 3, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-15, -1, 1, 7, 12],\n [0, -4, -8, -7, 8],\n [0, 0, 9, -6, 7],\n [0, 0, 0, 7, -10],\n [0, 0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 5, -2, -1, 2],\n [5, -6, -2, -7, 10],\n [-2, -2, -1, -10, -6],\n [-1, -7, -10, -1, 5],\n [2, 10, -6, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, -5, -14, 13, 9, -12],\n [0, -7, -9, 1, -1, 6],\n [0, 0, -14, -1, -4, 3],\n [0, 0, 0, -15, 7, 12],\n [0, 0, 0, 0, -6, 12],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 4, -10, -3, 11, -1],\n [0, 5, 14, 9, 0, 10],\n [0, 0, -6, 15, 1, 5],\n [0, 0, 0, -9, 0, -4],\n [0, 0, 0, 0, -2, 5],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, -15, 14, -3, -13, -10],\n [0, -15, -4, -15, -12, 13],\n [0, 0, 8, -2, -6, 12],\n [0, 0, 0, -14, 11, -15],\n [0, 0, 0, 0, -10, 4],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 4, 10, -8, 5, -2],\n [4, 11, 4, 8, -6, -8],\n [10, 4, 3, 5, -5, -6],\n [-8, 8, 5, 12, 5, 11],\n [5, -6, -5, 5, -4, -1],\n [-2, -8, -6, 11, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, 1, 4, -4, -8, -4],\n [1, -4, 7, 0, -1, -11],\n [4, 7, 9, -9, 11, 0],\n [-4, 0, -9, -7, 0, -6],\n [-8, -1, 11, 0, -11, -6],\n [-4, -11, 0, -6, -6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2699", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, 4, 2, 6, 4, 3],\n [4, -11, -8, 10, -6, -1],\n [2, -8, -14, -2, 10, -6],\n [6, 10, -2, -12, 8, 8],\n [4, -6, 10, 8, 7, 6],\n [3, -1, -6, 8, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 2, 0, -8, 1, 1],\n [2, -8, -4, 0, 4, 4],\n [0, -4, -10, -2, 0, 9],\n [-8, 0, -2, 8, -12, -10],\n [1, 4, 0, -12, 2, -4],\n [1, 4, 9, -10, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-180", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the inverse of matrix 1/180 * A where A =\n[[10, 7, 1, -6, -14, -5],\n [-2, -1, 9, 12, -14, -3],\n [11, 8, -14, 7, -7, 5],\n [-14, 12, 3, -15, -3, 15],\n [4, 11, -3, 9, -6, -2],\n [-8, 15, 4, -8, 3, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -13, -2, -10, -14, -2],\n [-8, 12, 0, -3, 11, 4],\n [13, -14, 9, 10, 2, -11],\n [-15, -7, 7, 13, 11, 9],\n [-6, 0, -11, -7, 13, -15],\n [0, -12, 1, -5, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14446", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 8, 10, -5, -3, 4],\n [-5, 9, 4, -12, -7, 10],\n [-1, 13, -15, -9, -5, -12],\n [1, 6, 13, 9, -5, -5],\n [-15, 6, -15, -1, -15, -10],\n [-15, -14, -4, 0, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -5, 15, 13, -3, -8],\n [2, 14, 10, 2, 2, -9],\n [-2, -12, -5, 10, -14, -4],\n [-5, -13, -5, 5, 10, -5],\n [-7, 2, 15, -3, -8, -9],\n [1, -10, -12, -15, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 2, -14, -1, 7, 14],\n [-10, -10, 0, -11, 8, -15],\n [3, -10, -5, 5, -7, -2],\n [9, -13, 14, -15, 12, 11],\n [-5, -7, 11, 11, -3, -3],\n [12, 8, 8, 14, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 11, -5, -14, 13, -15],\n [0, -13, 9, -10, 15, 8],\n [0, 0, 1, -2, -4, 12],\n [0, 0, 0, -8, 2, -11],\n [0, 0, 0, 0, -5, -7],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-455", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -10, -6, -5, 6, -4],\n [-10, -8, -5, -2, 1, -8],\n [-6, -5, 12, 0, -8, 4],\n [-5, -2, 0, -7, -1, 0],\n [6, 1, -8, -1, -1, 7],\n [-4, -8, 4, 0, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -15, -10, 2, 0, 6],\n [-15, -1, 8, -4, 9, 6],\n [-10, 8, -6, 12, 2, -6],\n [2, -4, 12, -6, 0, 7],\n [0, 9, 2, 0, 14, 6],\n [6, 6, -6, 7, 6, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, 9, -12, -3, 6, 12],\n [0, 5, 4, -6, 2, -11],\n [0, 0, -7, 8, 6, -1],\n [0, 0, 0, -15, 7, -10],\n [0, 0, 0, 0, -4, 9],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -3, 8, -6, -2, 4],\n [-3, -11, 2, 2, -4, 9],\n [8, 2, -7, 12, -10, -5],\n [-6, 2, 12, -13, 6, 2],\n [-2, -4, -10, 6, -11, 0],\n [4, 9, -5, 2, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 14, -12, 11, 14, 11],\n [13, 3, 14, 3, -12, 15],\n [2, -8, -15, 15, -3, -15],\n [10, 3, -1, -9, 14, -4],\n [-4, 10, -12, 14, -1, 14],\n [14, 10, 7, 11, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-199", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -2, 0, 2, -13, -2],\n [-2, -10, -14, 4, -1, -6],\n [0, -14, 3, 0, -5, -2],\n [2, 4, 0, 15, -4, 4],\n [-13, -1, -5, -4, -7, -2],\n [-2, -6, -2, 4, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 6, -2, -9, -15, 9],\n [0, -8, -8, 7, -2, -1],\n [0, 0, 7, 8, -8, -6],\n [0, 0, 0, -12, 7, 14],\n [0, 0, 0, 0, 9, -11],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-149", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, 8, 0, 2, -4, -2],\n [8, -12, -12, -4, -3, 2],\n [0, -12, -13, -2, 7, 6],\n [2, -4, -2, -9, -2, 6],\n [-4, -3, 7, -2, 12, 4],\n [-2, 2, 6, 6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, 6, 14, 10, -5, 10],\n [0, -15, -5, 4, 4, 2],\n [0, 0, -15, 0, -10, -10],\n [0, 0, 0, 1, -6, -8],\n [0, 0, 0, 0, -3, 8],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3986", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[15, -14, 14, -9, -14, -6],\n [0, 5, 6, -13, -1, 12],\n [0, 0, -3, -8, 10, 6],\n [0, 0, 0, 8, -10, -15],\n [0, 0, 0, 0, -8, -15],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[9, 11, -10, 2, 9, 3],\n [-8, 14, 4, 10, -2, -5],\n [5, -13, -5, -9, 10, 15],\n [12, 10, -11, 1, 7, -7],\n [-8, -10, -3, 2, 3, 0],\n [-15, -11, 15, -15, -1, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-9, -8, 2, -11, -3, 0],\n [-8, 9, -1, -3, -1, -10],\n [2, -1, -2, 0, 4, 11],\n [-11, -3, 0, 2, 2, -5],\n [-3, -1, 4, 2, 1, 2],\n [0, -10, 11, -5, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, 6, 2, -2, 0, 0],\n [6, -6, 4, -1, -3, 12],\n [2, 4, 1, 4, -6, -4],\n [-2, -1, 4, 15, -14, 8],\n [0, -3, -6, -14, 11, -8],\n [0, 12, -4, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 7, 4, -4, -14, -12],\n [0, 6, 11, -12, 9, 14],\n [0, 0, -11, -10, 14, -11],\n [0, 0, 0, 4, 12, -3],\n [0, 0, 0, 0, -1, -15],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-121", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, -15, 11, -12, 3, -3],\n [0, 12, -5, 7, -11, 9],\n [0, 0, -2, 3, -9, -11],\n [0, 0, 0, -1, -1, -7],\n [0, 0, 0, 0, 12, 14],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1046", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -12, -6, -8, -7, -15],\n [-9, -13, -6, 5, 14, -4],\n [5, 10, -8, 4, 7, 4],\n [-1, 8, -9, 9, -14, 5],\n [-7, 14, -13, -5, 4, -4],\n [-10, -1, 7, 6, 15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-223", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[11, -13, -13, -4, -11, -11],\n [0, 13, -12, -7, -3, 5],\n [0, 0, 8, 1, -1, -1],\n [0, 0, 0, -13, -2, -10],\n [0, 0, 0, 0, 6, -13],\n [0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -13, 5, -13, 7, 9],\n [0, -6, -12, -6, 5, -7],\n [0, 0, 4, 5, -5, 8],\n [0, 0, 0, 3, -3, -14],\n [0, 0, 0, 0, 10, -5],\n [0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4815", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 4, -11, -12, -2, 2],\n [0, 8, 15, 6, 12, 9],\n [0, 0, -14, -3, 11, 12],\n [0, 0, 0, 1, 9, -7],\n [0, 0, 0, 0, -11, 2],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-7, 4, 1, 9, 0, 2],\n [4, -10, 1, -2, 11, -2],\n [1, 1, -7, -4, -6, 5],\n [9, -2, -4, 7, 0, -8],\n [0, 11, -6, 0, -4, 6],\n [2, -2, 5, -8, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[1, -6, 4, -11, 2, 4],\n [-6, -12, 4, 0, -2, 10],\n [4, 4, -8, -2, -8, -6],\n [-11, 0, -2, 2, -4, 8],\n [2, -2, -8, -4, -15, -5],\n [4, 10, -6, 8, -5, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-5, 0, -13, 12, 1, 10],\n [0, -8, 4, 15, 2, -11],\n [0, 0, 6, -2, -15, 6],\n [0, 0, 0, -3, 12, -14],\n [0, 0, 0, 0, -6, 12],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, 10, 3, -15, 0, 11],\n [0, 4, 14, -6, 9, -1],\n [0, 0, -5, 7, 6, 1],\n [0, 0, 0, 10, 3, -12],\n [0, 0, 0, 0, -6, 4],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[5, 11, 1, -9, -6, -4],\n [11, -4, 0, -2, -2, -14],\n [1, 0, -9, -10, 1, 2],\n [-9, -2, -10, 13, 0, -10],\n [-6, -2, 1, 0, 15, 4],\n [-4, -14, 2, -10, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -10, 1, 1, 9, 3],\n [0, 1, -14, 5, -7, -7],\n [0, 0, 4, -8, 2, -9],\n [0, 0, 0, 6, -11, 5],\n [0, 0, 0, 0, -6, -12],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2910", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[4, -14, 1, 15, -1, -9],\n [0, 1, 9, 10, 7, -13],\n [0, 0, -8, -9, -2, 13],\n [0, 0, 0, 10, -3, -10],\n [0, 0, 0, 0, 9, 2],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "630", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 7, 8, 6, 11, 5],\n [0, -6, 7, 11, -9, 11],\n [0, 0, 7, -8, 11, 8],\n [0, 0, 0, -7, 1, -3],\n [0, 0, 0, 0, 8, 11],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-15, -10, 12, 15, 15, 4],\n [0, -3, -11, 7, -10, -8],\n [0, 0, 15, -6, -14, 7],\n [0, 0, 0, -13, 15, 9],\n [0, 0, 0, 0, 5, 2],\n [0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[5, 6, 0, 6, -7, 5],\n [5, 3, 7, -2, 6, -12],\n [7, 13, -4, 9, -3, -7],\n [10, 8, 13, 14, 4, 9],\n [0, -1, 1, 7, -14, 11],\n [14, -15, -13, -3, -14, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -8, -9, -6, -12, -7],\n [14, 9, -3, -2, 2, -13],\n [0, -14, 6, 9, -14, 7],\n [6, 5, 0, -6, -8, 6],\n [-9, -15, 14, -13, 15, 14],\n [-5, -5, 7, 9, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 10, -1, 1, 1, 4],\n [10, -10, 8, -3, -1, -5],\n [-1, 8, 4, -6, -14, -2],\n [1, -3, -6, 5, 2, -6],\n [1, -1, -14, 2, 15, -4],\n [4, -5, -2, -6, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "786", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 10, 4, -7, 11, 14],\n [-4, 9, -1, 7, -8, -4],\n [4, -4, 2, -15, -1, -7],\n [-12, 0, 7, -12, 14, 0],\n [15, 13, 6, 4, -10, 14],\n [-11, -12, 5, -5, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 5, -8, -15, 12, 12],\n [0, -1, 1, -8, 8, -8],\n [0, 0, 11, 15, -15, 14],\n [0, 0, 0, -15, -8, -12],\n [0, 0, 0, 0, -14, 10],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8260", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -14, -1, -7, 5, -11],\n [0, -12, -6, 4, 5, -12],\n [0, 0, 11, -9, -4, 2],\n [0, 0, 0, 14, 3, 13],\n [0, 0, 0, 0, 2, -2],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-14, 9, 14, -10, -14, -2],\n [0, -13, -6, 8, 0, 1],\n [0, 0, -15, -4, 5, 14],\n [0, 0, 0, 7, 13, 13],\n [0, 0, 0, 0, 11, -14],\n [0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, -2, -13, 0, 7, -15],\n [0, -13, -3, 10, 8, 4],\n [0, 0, 1, 12, 9, 9],\n [0, 0, 0, -6, 4, -6],\n [0, 0, 0, 0, -12, -4],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2902", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, -5, -13, 10, -4, 3],\n [14, 14, -8, 11, -4, 0],\n [8, 8, -8, -14, 13, 6],\n [-1, -5, 13, 6, -10, -9],\n [-12, 15, 13, -12, 13, -4],\n [12, 12, -3, 7, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-100", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[-7, -9, 0, -3, 15, 2],\n [0, 5, -6, -1, -3, 2],\n [-11, 9, -6, -8, -6, -14],\n [11, -7, 0, 10, 15, -12],\n [-11, 8, 1, -9, 0, -2],\n [10, 8, 3, -6, -15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, 11, 12, -4, -3],\n [-5, 5, -14, 2, 8, 9],\n [-11, -10, 6, -11, -3, -14],\n [-8, -3, 0, 15, -10, 8],\n [7, -12, -11, 2, 7, 13],\n [8, -9, -14, -1, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3886", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, -12, -15, 0, 7, -15],\n [8, -2, 12, -6, 12, -3],\n [-10, -5, -10, -10, 14, 14],\n [15, -13, -12, 7, -9, -5],\n [7, 8, 15, -2, -14, -10],\n [5, -5, -5, 1, 14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -12, 0, -12, 1, 12],\n [-12, 0, -4, -1, -10, 0],\n [0, -4, 2, 6, -2, -3],\n [-12, -1, 6, 14, 3, -7],\n [1, -10, -2, 3, 1, 2],\n [12, 0, -3, -7, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-470", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[-2, -8, 0, -5, 0, 4],\n [-8, 7, -4, -1, -2, -2],\n [0, -4, 7, -2, 8, -14],\n [-5, -1, -2, 13, 7, -4],\n [0, -2, 8, 7, 15, -1],\n [4, -2, -14, -4, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-2, 2, -14, 9, 3, -3],\n [6, -1, -5, 12, -13, 4],\n [15, -3, 3, 9, -1, -7],\n [-1, -1, 10, -12, 1, -14],\n [-9, -3, -5, -3, 13, -10],\n [-14, 13, 6, 6, 9, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (4, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 12, -2, -5, 1, -13],\n [-4, -13, 15, -3, -1, 4],\n [2, -15, -4, 7, 0, -13],\n [-11, 5, 8, -7, 15, -14],\n [14, -13, -15, 9, 11, -15],\n [0, 8, 13, 1, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, -4, 6, -1, 4, 10],\n [-4, -13, -14, -8, -10, 4],\n [6, -14, -3, -13, 4, -6],\n [-1, -8, -13, -14, 8, 2],\n [4, -10, 4, 8, -12, -2],\n [10, 4, -6, 2, -2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 10, 5, 8, -11, -4],\n [0, 6, 8, -11, -5, -13],\n [0, 0, 14, 8, 3, 10],\n [0, 0, 0, -3, -7, -10],\n [0, 0, 0, 0, 12, -12],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1023", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[2, -4, 0, 3, 10, 0],\n [-4, -1, -10, 4, 4, -2],\n [0, -10, -8, -6, -5, 4],\n [3, 4, -6, -13, -6, 2],\n [10, 4, -5, -6, -7, 3],\n [0, -2, 4, 2, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}